Category theorems for stable operators on Hilbert spaces
We discuss the two closely related, but different concepts of weak and almost weak stability for the powers of a contraction on a separable Hilbert space. Extending Halmos' and Rohlin's theorems in ergodic theory as a model, we show that the set of all weakly stable contractions is of firs...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2008
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| Sorozat: | Acta scientiarum mathematicarum
74 No. 1-2 |
| Kulcsszavak: | Matematika, Hilbert-tér |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16238 |
| Tartalmi kivonat: | We discuss the two closely related, but different concepts of weak and almost weak stability for the powers of a contraction on a separable Hilbert space. Extending Halmos' and Rohlin's theorems in ergodic theory as a model, we show that the set of all weakly stable contractions is of first category while the set of all almost weakly stable contractions is of second category and is residual. Analogous statements for unitary and isometric operators axe also proved. |
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| Terjedelem/Fizikai jellemzők: | 259-270 |
| ISSN: | 0001-6969 |